This paper studies optimal matroid partitioning problems for various objective functions. In the problem, we are given k weighted-matroids on same ground set. Our goal is to find a feasible partition that minimizes (maximizes) value of an function. A typical maximum over all subsets total weights elements in subset, which extensively studied scheduling literature. Likewise, as function, handle ...

Matroid theory is a generalization of the idea of linear independence. A matroid M consists of a finite set E (called the ground set) and a collection S of subsets of E satsifying the following conditions: (1) ∅ ∈ S; (2) if I ∈ S, then every subset of I is in S; (3) if I1 and I2 are in S and |I1| < |I2|, then there is an element e of I2 − I1 such that I1 ∪ e is in S. The elements of S are calle...

The independent sets of an algebraic matroid are sets of algebraically independent transcendentals over a field k. If a matroid M is isomorphic to an algebraic matroid the latter is called an algebraic representation of M. Vector representations of matroids are defined similarly. A matroid may have algebraic (resp. vector) representations over fields of different characteristics. The problem in...

In this paper, we introduce the problem of Matroid-Constrained Vertex Cover: given a graph with weights on edges and matroid imposed vertices, our is to choose subset vertices that independent in matroid, objective maximizing total weight covered edges. This generalization much studied max $k$-vertex cover problem, which simple uniform it also special case monotone submodular function under con...

Given a rank-r binary matroid we construct a system of O(r) linear equations in O(r) variables that has a solution over GF(2) if and only if the matroid is graphic.

We consider the matroid median problem (MMP), which is defined as follows. As in the uncapacitated facility location problem, we are given a set of facilities F and a set of clients D. Each facility i has an opening cost of fi. Each client j ∈ D has demand dj and assigning client j to facility i incurs an assignment cost of djcij proportional to the distance between i and j. Further, we are giv...

One of the foundations of oriented matroid theory is the topological representation theorem of Folkman and Lawrence [8]. It says that an oriented (simple) matroid can be realized uniquely as an arrangement of pseudospheres. That there is no similar interpretation for the class of all matroids has been taken for granted. For instance, “A non-coordinatizable matroid of abstract origin may be thou...